We examine the static non-linear optical response of monolayer transition metal dichalcogenides. Whereas the shift current is suppressed, we identify a strong, valley-dependent non-reciprocal response, which we term a textit{unidirectional valley-contrasting photo-current} (UVCP). It originates from Kramers symmetry breaking by trigonal warping, and its direction is set by the wave vector connecting the two valleys. The UVCP is proportional to the mobility and is enhanced by the excitonic Coulomb interaction and inter-valley scattering, enabling monitoring of inter-valley transitions. We discuss detection strategies in state-of-the-art experiments.
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